LIU, Qing

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LIU, Qing
Institut de Mathématiques de Bordeaux [IMB]

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Transactions of the American Mathematical Society. 2022

American Mathematical Society

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2022

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Given a hyperelliptic curve C of genus g over a number field K and a Weierstrass model {\mathsrc C} of C over the ring of integers O_K (i.e. the hyperelliptic involution of C extends to {\mathsrc C} and the quotient is a smooth model of P1_K over OK), we give necessary and sometimes sufficient conditions for {\mathsrc C} to be defined by a global Weierstrass equation. In particular, if C has everywhere good reduction, we prove that it is defined by a global Weierstrass equation with invertible discriminant if the class number hK is prime to 2(2g+1), confirming a conjecture of M. Sadek.< Leer menos

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GLOBAL WEIERSTRASS EQUATIONS OF HYPERELLIPTIC CURVES

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